Dan Fox

Publications and preprints

Articles are listed (roughly) in reverse chronological order. The publication date is sometimes several years after the article was posted to the ArXiv.

ArXiv versions are available for most of the articles listed below (they sometimes differ from the published versions in minor ways).

  1. Left symmetric algebras and homogeneous improper affine spheres. [arXiv:1707.08896].
  2. Symmetries of the space of linear symplectic connections. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 13 (2017), 002, 30 pages.
  3. Remarks on symplectic sectional curvature. Differential Geometry and its Applications. Vol. 50 (February 2017), pp. 52-70. [arXiv:1610.05898].
  4. Infinitesimal affine automorphisms of symplectic connections. Journal of Geometry and Physics. Vol. 106 (2016), pp. 210-212. [arXiv:1511.09258].
  5. Equiaffine geometry of level sets and ruled hypersurfaces with equiaffine mean curvature zero. Mathematische Nachrichten 290 (2017), no. 2-3, 293-320. [arXiv:1503.09108].
  6. Functions dividing their Hessian determinants and affine spheres. The Asian Journal of Mathematics. Vol. 20, No. 3, pp. 503-530, July 2016. [pdf] [arXiv:1307.5394].
  7. A Schwarz lemma for Kähler affine metrics and the canonical potential of a proper convex cone. Annali di Matematica Pura ed Applicata. February 2015, Vol. 194, Issue 1, pp. 1-42. [pdf]
  8. Critical symplectic connections on surfaces. [arXiv:1410.1468].
  9. Geometric structures modeled on affine hypersurfaces and generalizations of the Einstein Weyl and affine hypersphere equations. Extended Abstracts Fall 2013, Research Perspectives CRM Barcelona (Trends in Mathematics), 2015, Birkäuser Basel. pp. 15-19. (The typos in the references were added by the editors.)
  10. Ricci flows on surfaces related to the Einstein Weyl and Abelian vortex equations. Glasgow Mathematical Journal. Vol. 56, Issue 03 (Sept., 2014), pp. 569-599. [pdf]
  11. WHAT IS ... an affine sphere? Notices of the American Mathematical Society. March 2012, Vol. 59, Issue 3.
  12. Einstein-like geometric structures on surfaces. Annali della Scuola Normale Superiore, Classe di Scienze Vol. XII, issue 3 (2013) 499-585. [arXiv:1011.5723].
  13. Geometric structures modeled on affine hypersurfaces and generalizations of the Einstein Weyl and affine hypersphere equations.[arXiv:0909.1897]
  14. Projectively invariant star products. International Mathematics Research Papers 9 (2005), 461-510, 2005. [math.DG:0504596].
      (An [erratum] clarifies some ambiguities in the exposition.)
  15. Contact projective structures. Indiana University Mathematics Journal 54 (2005), 1547--1598. [math.DG:0402332]
      Note: In the statement of Theorem B, the assumption that the ambient connection is homogeneous is omitted, although it is assumed in the proof, and is necessary for the uniqueness.
  16. Contact Schwarzian derivatives. Nagoya Mathematical Journal 179 (2005), 163-187. [math.DG:0405369]
  17. Contact path geometries. [math.DG:0508343]
    • I intend someday to rewrite this article completely. The arXiv version contains some mostly inconsequential but potentially confusing misstatements.
The reviews of my articles on MathSciNet.
The reviews I have written for MathSciNet.

Warning: Because the circumstance still occasionally causes confusion, please be advised that there is another Dan Fox, about the same age as me, who has published, in some of the same journals, articles about topics in differential geometry similar to those I study, although it appears he now works primarily as a composer of music. My articles are signed as Daniel J. F. Fox, his as Daniel Fox, although we both are called Dan.